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Question 1189458: For the polynomial Function : F(x)=-2(x + 1/2) (x+4)^2
a)List each real zero and its multiplicity:
b)Determine whether graph crosses or touches the x-axis at each x-intercept:
c)Determine the behavior of the graph near each x-intercept(zero):
d)Determine the maximum number of turning point on the graph:
e)Determine the end behavior, that is finding the power function that the graph of
f resembles for large values of |x|:
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
For the polynomial Function :
a)List each real zero and its multiplicity:
if  => ,..... multiplicity 1
if  => ,..... multiplicity 2
b)Determine whether graph crosses or touches the x-axis at each x-intercept:
For zeros with multiplicities, the graphs  or are tangent to the x-axis at these x-values.
For zeros with  multiplicities, the graphs  or intersect the x-axis at these x-values.
have an multiplicity => the graph will the x-axis
have an multiplicity=> the graph will the x-axis
c)Determine the behavior of the graph near each x-intercept(zero):
Since the leading term of the polynomial (the term in the polynomial which contains the highest power of the variable) is  , the degree is  , i.e. even, and the leading coefficient is  , i.e. negative.
This means that f(x)→ ∞ as x→ -∞ , f(x)→ -∞ as x→ ∞
d)Determine the maximum number of turning point on the graph:
The maximum number of turning points of a polynomial function is always one less than the degree of the function.
This function f is a th degree polynomial function and has  turning points.
e)Determine the end behavior, that is finding the power function that the graph of
f resembles for large values of | |:
If we expand we get
 ..... the dominating term
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